What an amortization schedule shows
A fixed-rate mortgage has one payment amount and 360 different payments. The dollar figure never changes, but the split inside it moves every month, and the schedule is the table that records that movement.
The mechanism is simple enough to do on paper. Interest is charged only on money you currently owe, so the lender takes the balance standing at the start of the month, multiplies it by one twelfth of the annual rate, and that product is the interest portion. Whatever is left of your payment reduces the balance. Next month the balance is smaller, so the interest slice is smaller, so more of an identical payment goes to principal. The process compounds gently in your favour, and the schedule makes it visible.
Three consequences fall straight out of that arithmetic, and they surprise most borrowers. Early payments are almost entirely interest — on a 6.5% thirty-year loan, 86% of the first payment. The crossover payment, where principal first exceeds interest, arrives far later than the halfway point of the term. And total interest over thirty years can exceed the amount borrowed outright, which is why the term matters as much as the rate.
The schedule is also the document you need for practical tasks: proving the balance on a given date for a home-equity application, working out how much equity you have built for a refinance decision, or checking a servicer's payoff quote.
The recurrence, and the closed form that skips ahead
Every row of the schedule comes from three lines. Write Bk−1 for the balance before payment k, r for the monthly rate and M for the payment:
Interest_k = B_(k−1) × r, then Principal_k = M − Interest_k, then B_k = B_(k−1) − Principal_k.
The payment itself comes from the amortised-loan formula, M = P·r / (1 − (1 + r)−n), which is exactly the value that drives the balance to zero on payment n and not a month sooner or later. The same figure is what the mortgage payment calculator produces.
You do not have to iterate 360 times to reach a single row. The balance after payment k is the present value of the payments that remain: Bk = M · (1 − (1 + r)−(n−k)) / r. That closed form is how a servicer quotes a payoff figure without printing the whole table, and it is what this calculator checks its iteration against.
The crossover payment has a closed form too, and it is a genuinely elegant one. Principal exceeds interest when M − B·r > B·r, that is when the balance falls below M/(2r). Substituting the closed form for the balance gives the crossover at payment ⌈n + 1 − ln 2 / ln(1 + r)⌉. Notice what is missing: the loan amount. Crossover depends only on the rate and the term, never on how much you borrowed. A $150,000 loan and a $900,000 loan at the same rate and term cross over on the same payment number.
Worked example: $350,000 at 6.5% over 30 years
Take the default loan and build the first two rows by hand.
- Monthly rate. r = 6.5 ÷ 100 ÷ 12 = 0.005416667.
- Payment count. n = 30 × 12 = 360.
- Discount factor. (1.005416667)360 = 6.99180, so (1 + r)−360 = 0.1430252 and 1 − that = 0.8569748.
- Payment. M = 350,000 × 0.005416667 ÷ 0.8569748 = 1,895.83 ÷ 0.8569748 = $2,212.24.
- Payment 1. Interest = 350,000 × 0.005416667 = $1,895.83. Principal = 2,212.24 − 1,895.83 = $316.41. New balance = $349,683.59.
- Payment 2. Interest = 349,683.59 × 0.005416667 = $1,894.10. Principal = 2,212.24 − 1,894.10 = $318.14. New balance = $349,365.45.
The principal slice grew by $1.73 in one month, and it keeps growing by a little more each time. Run it out and the totals are these: interest over the full term is 360 × 2,212.24 − 350,000 = $446,406, more than the amount borrowed. The balance after five years is 2,212.24 × (1 − 1.005416667−300) ÷ 0.005416667 = $327,639 — you will have paid $132,734 and reduced the debt by $22,361. And the crossover lands on payment ⌈361 − 0.6931 ÷ 0.0054020⌉ = ⌈361 − 128.31⌉ = payment 233, which is 19 years and 5 months in.
How to read your own schedule
Read the yearly summary table first, because it answers the question most people actually have: how much of what I paid this year went anywhere useful. In year one of the example above, $3,912 of $26,547 paid reduced the debt. That ratio is not a scandal — it is the arithmetic of charging interest on an outstanding balance — but it does explain why selling in year three rarely leaves the equity people expect.
Then look at the crossover figure. Because it depends only on rate and term, it is a clean way to compare loan structures. At 6.5% a thirty-year loan crosses over on payment 233 of 360, roughly 65% of the way through; a fifteen-year loan at the same rate crosses on payment 53 of 180, under a third of the way through. That is the real difference between the two products, and it is more informative than comparing monthly payments.
Use the balance lookup for anything date-driven. Lenders drop private mortgage insurance when the scheduled balance reaches 78% of original value, and the schedule tells you which payment that is. Home-equity lines are sized against a balance. Capital-gains planning on a sale needs the payoff figure, not the original loan.
Finally, notice what any extra principal does. Because interest is charged on the balance, a dollar paid early removes r dollars of interest from every remaining month — so the earlier a prepayment lands, the more it is worth. The extra payment payoff calculator quantifies that directly, and the extra-principal field here lets you see the effect on the schedule itself.
Crossover payment number by rate and term
| Annual rate | 15 years (of 180) | 20 years (of 240) | 30 years (of 360) |
|---|---|---|---|
| 5.0% | 15 | 75 | 195 |
| 5.5% | 30 | 90 | 210 |
| 6.0% | 43 | 103 | 223 |
| 6.5% | 53 | 113 | 233 |
| 7.0% | 62 | 122 | 242 |
| 7.5% | 70 | 130 | 250 |
| 8.0% | 77 | 137 | 257 |
Read down a column and the crossover arrives later as the rate rises; read across a row and each five years of extra term pushes it back by exactly 60 payments, because the same quantity ln 2 / ln(1 + r) is subtracted from a larger n.
Things that make a real schedule differ from this one
- Escrow is not in here. This schedule covers principal and interest only. Your servicer collects property tax and insurance alongside it and adjusts the escrow portion annually, so the amount drafted from your account will not match the payment shown.
- Cent rounding. Servicers round the payment to the cent and carry the difference, so a real ledger drifts from an unrounded schedule by a few dollars over thirty years and the final payment is adjusted to clear the balance exactly.
- Interest is calculated on the date received, not the due date. Most US mortgages accrue monthly in arrears on a 30-day convention, but a payment posted late accrues extra days on some notes. Check whether yours is a simple-interest daily accrual mortgage — schedules for those differ.
- Adjustable-rate loans re-amortise. After the fixed period an ARM recalculates the payment from the new rate over the remaining term. A single schedule cannot describe it past the first adjustment.
- Extra principal must be applied as principal. Servicers frequently hold unlabelled extra money as a prepaid next payment instead. Write “apply to principal” on the instruction and check the following statement.
- Biweekly plans are not what they look like. Paying half the payment every two weeks produces 26 half-payments, which equals 13 monthly payments a year — the saving comes from the thirteenth payment, not from the fortnightly timing.
Where amortization schedules come from and what else uses them
The constant-payment amortised loan is not specific to mortgages. It is the same annuity mathematics behind an auto loan, a personal loan and the standard ten-year student loan repayment plan. Change the rate and the number of periods and the same three lines generate every one of those schedules.
What is specific to US mortgages is the disclosure around them. Regulation Z, which implements the Truth in Lending Act, requires a closed-end mortgage disclosure that includes a payment schedule and an APR computed under a prescribed method — and the APR is not the note rate, because it folds in points and certain fees. Building a schedule from the APR overstates both the payment and the interest, which is the single most common error in home-made amortization spreadsheets.
Revolving credit works differently and cannot be amortised this way at all. A credit card has no fixed term, so the payoff horizon depends on what you choose to pay; the credit card payoff calculator solves for the number of months instead of assuming it. Negative-amortisation products invert the logic entirely — when the payment is smaller than the accrued interest, the balance rises, and no schedule of the kind above exists.
Key terms
- Amortisation
- Retiring a debt through equal periodic payments, each split between interest on the outstanding balance and a reduction of that balance.
- Crossover payment
- The first payment in which the principal portion exceeds the interest portion. It depends on the rate and the term only, not on the loan amount.
- Payoff figure
- The amount required to clear the loan on a given date: the scheduled balance plus interest accrued since the last payment, and sometimes a recording fee.
- In arrears
- Interest charged for the period just ended rather than the one about to begin. Your 1 June mortgage payment covers May's interest, which is why closing statements prorate interest to the end of the closing month.